Set-up

Clear Environment

• always start a new script with a clear R environment
  • no objects stored in the Environment
  • no packages loaded
• click Session > Restart R to start with a fresh environment
  • or the keyboard shortcut Cmd/Ctrl+Strg+0

Packages

pacman::p_load(tidyverse,
               here,
               janitor)

Load data

• two datasets today:
  • groesse_geburtstag_ws2324.csv: a slightly changed groesse_geburtstag dataset from last week
  • languageR_english.csv: condensed version of english dataset from the languageR package
• if you don’t have these data already, download them from Moodle

df_groesse <- read_csv(here("daten", "groesse_geburtstag_ws2324.csv"))

df_eng <- read_csv(here("daten", "languageR_english.csv")) |> 
  clean_names() |> 
  # fix some wonky variable names:
  rename(rt_lexdec = r_tlexdec,
         rt_naming = r_tnaming)

Deskriptive statistics

• quantitatively describe the central tendency, variability, and distribution of data
  • also called summary statistics
• e.g., range of values (minimum, maximum), the mean value, and the standard deviation

Number of observations (\(n\))

• not a statistic, but is important information
  • more data (higher \(n\)) = more evidence
  • less data (lower \(n\)) = may not be generalisable to the broader population
• nrow(): get number of observations in a dataset

nrow(df_groesse)

[1] 9

Measures of central tendency

• quantitavely describe the centre of our data
  • the mean, median, and mode

Mean (\(\mu\))

• the mean, or average: the sum of all values divided by the number of values (as in Equation \(\ref{eq-mean}\))

\[\begin{align} \mu &= \frac{sum\;of\;values} {n} \label{eq-mean} \end{align}\]

Median

• the value in the middle of the dataset
• if you line up your data in order of value, half of the data lie below the median, and half above it

The median is robust, the mean is not

• the median is not affected by outliers/extreme values (unlike the mean)
  • what happens to the mean and median when we change our tallest height (190cm) to be the height of the current tallest person in the world: 251 cm?

df_groesste <- 
  df_groesse |> 
  mutate(groesse = ifelse(groesse == 190, 251, groesse))

sort(df_groesste$groesse)

[1] 163 164 167 167 170 171 182 189 251

median(df_groesste$groesse)

[1] 170

mean(df_groesste$groesse)

[1] 180.4444

• the median is often reported instead of the mean for data that has heavy skews to more extreme values, such as when reporting incomes in a population

Mode

• the value that occurs the most in a data set
• no R function to determine the mode
  • but we can visualise it, e.g., with a histogram or a density plot

df_groesse |>
  ggplot(aes(x = groesse)) +
  geom_histogram(binwidth = .5) +
  theme_minimal() 

Measures of dispersion

• describe the spread of data points
  • tell us something about how the data whole is distributed

Range

• can refer to the highest (maximum) and lowest (minimum) values
  • or the difference between highest and lowest value

Standard deviation (sd or \(\sigma\))

• a measure of how dispersed data is in relation to the mean
  • a low standard deviation means data are clustered around the mean (i.e., there is less spread)
  • a high standard deviation means data are more spread out
• standard deviation is very often reported whenever mean is reported

Summary statistics with R

• the dplyr package from the tidyverse has some helpful functions to produce summary statistics
• let’s now use the df_eng dataset to learn about these dplyr verbs.

dplyr::summarise

• summarise() function (dplyr) computes summaries of data
  • but we have to tell it what to compute, and for which variable(s)
• for example, the n() function produces the number of observations (only when used inside summarise() or mutate())

df_eng |>
  summarise(N = n())

# A tibble: 1 × 1
      N
  <int>
1  4568

Grouping variables

• we usually want to compare certain groups
  • e.g., comparing groesse between L1 speaker groups

.by =

• the .by = argument in summarise() computes our calculations on groups within a categorical variable

df_eng |>
  drop_na() |>
  summarise(mean_lexdec = mean(rt_lexdec),
            sd_lexdec = sd(rt_lexdec),
            N = n(),
            .by = age_subject) |>
  arrange(mean_lexdec)

# A tibble: 2 × 4
  age_subject mean_lexdec sd_lexdec     N
  <chr>             <dbl>     <dbl> <int>
1 young              630.      69.1  2283
2 old                787.      96.2  2284

Group by multiple variables

• we can also group by multiple variables
  • for this we need concatenate (c())
• we’ll filter to only have a couple of carriers, just so our output isn’t too long

Anscombe’s Quartet

• Francis Anscombe constructed 4 datasets in 1973 to illustrate the importance of visualising data before analysing it and building a model
• these four plots represent 4 datasets that all have nearly identical mean and standard deviation, but very different distributions

DatasaurRus

• datasauRus package (Davies et al., 2022) contains some more datasets that have similar mean and sd, but different distributions
  • given in Tabelle 2

pacman::p_load("datasauRus")

Aufgaben